Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | #126×#261 |
| Fitting | C13×#126 ⋊ C4 |
| Sylow | C13 ⋊ C4×#126 |
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#126×#261, #261×#529, #261×#538, … |
| maximal normal subgroup of | C2×#126×#261, #261×#529, #261×#538, … |
| maximal quotient of | #261×#388, #261×#387, #261×#383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20978);